NEW YORK (CNN/Money) -
The U.S. union movement split apart this week over how to best organize workers at non-union companies.

Two of the largest unions left the AFL-CIO this week, and others are threatening to follow.

But even without the defections, the battle for new recruits is an uphill one.

While unions have sometimes found willing managements in the public sector, employer hostility to organizing campaigns is the rule in the private sector.

But that doesn't stop the unions from trying, especially with union membership now down to about one out of every 12 private-sector employees.

From talking to professors, union officials and other experts, here are the companies that are on the top of organized labor's wish list.

Wal-Mart Stores

The largest private-sector employer in the country with 1.3 million employees, Wal-Mart is by far the biggest target for labor. And so far it has been among the most unattainable.

Unions have won the right to hold organizing votes at only a few Wal-Mart locations. The only time that a union won a vote was in 2000 -- 10 butchers signed on for representation at a Jacksonville, Texas store. Two weeks later, Wal-Mart got rid of all its butcher operations nationwide.

Most recently, in February, Wal-Marttire and lube shop employees in Loveland, Colo., and New Castle, Pa., voted against representation.

At this point, the union efforts at Wal-Mart are focused on building community pressure rather than getting employees to sign union cards, said Jim Papian, spokesman for the United Food and Commercial Workers union, one of the insurgent groups boycotting this week's AFL-CIO convention.

"There is no way I can put a time line on when this or that will happen," he said of the next organizing vote at Wal-Mart. "We are coalescing civil rights groups, women's groups, community groups, drawing attention to Wal-Mart's practices. When we get the critical mass, then we'll start seeing what happens."

Wal-Mart says that its nationwide average hourly pay for full-time employees is $9.68 an hour. The United Food and Commercial Workers union argues the rate averages only $8.23 an hour, citing what it said is independent expert statistical analysis.

The Bureau of Labor Statistics estimates that the average hourly wage for all non-supervisory retail employees nationwide is $12.34.

Wal-Mart spokesman Dan Fogleman says the government data is inflated by overtime, and that Wal-Mart's pay scale is competitive and in many cases higher in every market it operates in.

"If you look at where our stores are, we have an awful lot of rural stores [where average wages are lower]," he said.

FedEx

FedEx (Research) is essentially a non-union company, with only its pilots represented by a union.

While UPS has continued to thrive even while paying union pay and benefit levels, many unionized trucking companies have gone out of business.

The unions have an extra hurdle in attempting to organize FedEx, however, because express carriers operate under different labor law than most companies.

Under that law, a union would have win a vote of all FedEx employees in certain job classification, such as delivery driver or package sorter, rather than trying to win a series of votes at specific facilities, which is the more typical organizing method.

FedEx Express, its core overnight operation, has about 139,000 employees, the overwhelming majority in the United States.

Verizon Wireless

Unions have very good representation within the traditional land-line phone companies. But they have been much slower making inroads among providers of wireless communications.

Cingular marks the unions' only significant private sector organizing success story of the past decade. Out of 63,300 U.S. employees, Cingular has almost 22,000 workers represented by the Communications Workers of America.

Unions have not had as much luck at Verizon Wireless, a joint venture between Verizon Communications (Research) and Vodafone, which has nearly 50,000 employees.

"CWA has made progress organizing some wireless workers. (Verizon Wireless) is probably the target with the best shot right now," said Ross Eisenbrey, a vice president of the Economic Policy Institute, a liberal research institute specializing in labor market policies.

Toyota, Honda or Nissan

Today, Japanese automakers have 25 plants in North America, employing about 56,000 employees, and more are planned.

With the Big Three looking to shrink capacity and trim staff, it is essential for the United Auto Workers to make a breakthrough with these so-called "transplants" assembly plants.

So far it has come up empty, losing a vote at a Nissan plant in Smyrna, Tenn. in October 2001.

"There are organizers at a number of foreign-owned auto plants in the South. They're putting together committees, identify leadership, training workers," said Stewart Acuff, the AFL-CIO's director of organizing. "These will be long fights."

Comcast and IBM

Comcast (Research), the nation's largest cable operator is primarily non-union. But the Communications Workers of America is making a concerted effort at a number of Comcast locations around the nation.

The company has about 59,000 employees in its cable and Internet operations.

Comcast says that unions represent about 1,500 of those employees, down from 3,600 when the company completed its purchase of AT&T Cable in 2002.

While the union has been holding organizing elections, Comcast has been pushing for union decertification elections during the same period.

The CWA also has an effort at IBM (Research) that got its start when the computer maker announced plans to change its pension plans in 1999 from a traditional plan that paid a fix amount per month as long as a retiree lived to one paid a lump sum.

But after IBM made some changes to answer criticisms of that shift, some of the union efforts there calmed down, said Marcus Courtney, president of WashTech, the high tech organizing arm of CWA.

"The Alliance at IBM is still an active campaign, but we've not been able to build enough support to get to the point to have a vote," said Courtney. "But the pension changes there, or the cutbacks and pension changes just announced at Hewlett Packard show the need for unions. They're unilateral, with no one in position to speak for the employees being affected."